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If three acute angles of a quadrilateral measure 70° each, then the measure of the fourth angle is___________________.

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Last updated date: 23rd Jul 2024
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Answer
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Hint: Study the property of the quadrilateral. Learn about the measure of the four angles of the quadrilateral. The measure of four angles of a quadrilateral is 360 degrees.
Formula used: The sum of the four angles of a quadrilateral ABCD is, \[\angle A + \angle B + \angle C + \angle D = {360^ \circ }\] where, \[\angle A,\angle B,\angle C\] and \[\angle D\] are the four angles of the quadrilateral.

Complete step by step solution:
We have given here a quadrilateral whose three angles are acute angles. Measure of each angle of the quadrilateral is \[{70^ \circ }\] . We have to find the measure of the fourth angle.
Now, we know that the sum of the four angles of a quadrilateral ABCD is, \[\angle A + \angle B + \angle C + \angle D = {360^ \circ }\] where, \[\angle A,\angle B,\angle C\] and \[\angle D\] are the four angles of the quadrilateral.
So, the sum of three angles of the quadrilateral given here is,
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 \[\angle A + \angle B + \angle C = {70^ \circ } \times 3 = {210^ \circ }\] [ Let, four angles are \[\angle A,\angle B,\angle C\] and \[\angle D\] respectively]
So, the fourth angle of the quadrilateral is the difference between 360 and the sum of the three angles. \[\angle D = {360^ \circ } - (\angle A + \angle B + \angle C)\]
Or, \[\angle D = {360^ \circ } - {210^ \circ } = {150^ \circ }\]
So, the measure of the fourth angle is \[{150^ \circ }\]
So, the correct answer is “ \[{150^ \circ }\] ”.

Note: The sum of the three angles of a triangle is \[{180^ \circ }\] and the sum of the four angles of a quadrilateral is always equal to \[{360^ \circ }\] . For different types of quadrilaterals with the said property they have additional properties. For example, the sum of opposite angles of a quadrilateral inside a circle is \[{180^ \circ }\] . Each angle of a square is a right angle. The opposite angle of a parallelogram is equal.